The main input parameters are (i) the dust temperature at the inner shell boundary (\(T_{\mathrm {d}}\) ), (ii) the total radial optical depth at 0.55\(\)  (\(\tau _V\) ), (iii) the shell density (iv) the grain-size distribution for a choice of grain composition, (v) the relative shell thickness (\(Y\)  = ratio of the shell's outer radius, \(R_{ou}\) , to its inner radius, \(R_{in}\) ), (vi) the spectrum of the central star. The shell density was assumed to be a single power-law exponent, \(n\) , of the power-law (\(\rho _d(r)\propto r^{-n}\) ), or a combination of two power-laws (described below). We have computed the stellar spectrum using the Tübingen NLTE Model Atmosphere Package (TMAP) ([1]}, [2]}, [3]}) for \(T_{eff}=105,000\)  K – as derived by [4]} using photoionization modeling. We have accounted for nebular extinction by using a visual extinction of \(A_V=0.31\)  – derived by [5]}) – to attenuate and redden the model SED.
